DRESSIANS, TROPICAL GRASSMANNIANS, AND THEIR RAYS

By Sven Herrmann, Michael Joswig, David E. Speyer. 2011

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SVEN HERRMANN, MICHAEL JOSWIG, AND DAVID SPEYERAbstract. The Dressian Dr(k;n) parametrizes all tropical linear spaces, and it carriesa natural fan structure as a subfan of the secondary fan of the hypersimplex ( k;n). Weexplore the combinatorics of the rays of Dr(k;n), that is, the most degenerate tropicalplanes, for arbitrary k and n. This is related to a new rigidity concept for con gurationsof n k points in the tropical (k 1)-torus. Additional conditions are given for k = 3.On the way, we compute the entire fan Dr(3;8).

Subfields: Algebra and Number Theory, Computational Mathematics, Computational Theory and Mathematics

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